Chapter : Linear equations
Lesson : Math of Junior High School
2x - 3 + 3x = -28
= 5x - 3 = -28
= 5x = -28 + 3
= 5x = -25
= x = -25 / 5
= x = 5
For this case we must find the value of "x" of the following expression:
[tex]2x-3 + 3x = -28[/tex]
We add similar terms:
[tex]5x-3 = -28[/tex]
We add 3 to both sides of the equation:
[tex]5x = -28 + 3[/tex]
Different signs are subtracted and the sign of the major is placed:
[tex]5x = -25[/tex]
We divide between 5 on both sides of the equation:
[tex]x = \frac {-25} {5}\\x = -5[/tex]
ANswer:
[tex]x = -5[/tex]
You want to produce a scale drawing of your living room, which is 24 ft by 15 ft. If you use a scale of 4 in. = 6 ft, what will be the
dimensions of your scale drawing?
Answer:
The dimensions of the living room is the scale drawing are 16 in by 10 in
Step-by-step explanation:
we know that
The scale drawing is equal to
[tex]\frac{4}{6}\frac{in}{ft}[/tex]
That means ----> 4 inches in the drawing represent 6 feet in the real
so
Find the dimensions of the living room in the scale drawing
using proportion
For 24 ft
[tex]\frac{4}{6}\frac{in}{ft}=\frac{L}{24}\frac{in}{ft}\\ \\L=4*24/6\\ \\L=16\ in[/tex]
For 15 ft
[tex]\frac{4}{6}\frac{in}{ft}=\frac{W}{15}\frac{in}{ft}\\ \\L=4*15/6\\ \\W=10\ in[/tex]
therefore
The dimensions of the living room is the scale drawing are 16 in by 10 in
What type of number can be written as a fraction plq, where p and q are integers
and q is not equal to zero?
A. 7
B. All numbers can written in this way
C. A rational number is
D. An irrational number
Answer:
rational number
Step-by-step explanation:
written as a fraction p/q, where p and q are integers and q is not equal to zero, is called as rational numbers. Example - 4/5, 2, 100, 1/7 etc all are rational numbers.
Which set of ratios could be used to determine if one triangle is a dilation of the other
Final answer:
To determine if one triangle is a dilation of another, ratios of corresponding sides must be compared and set up as proportions to see if they are equivalent. When the proportions are equivalent, it indicates a consistent scale factor, confirming a dilation.
Explanation:
To determine if one triangle is a dilation of the other, we compare the ratios of corresponding sides from each triangle. A dilation occurs when all sides of one triangle are in proportion with the sides of a second triangle by the same scale factor. For example, if one triangle has sides of length 3, 4, and 5, and the second triangle has sides of length 6, 8, and 10, then the ratios of the corresponding sides (3/6, 4/8, 5/10) all simplify to 1/2, indicating that the second triangle is a dilation of the first.
To use ratios to determine if one triangle is a dilation of another, you need to set up proportions. For instance, we can express the ratios of corresponding lengths as fractions, and then set each of these ratios equal to the unit scale to form proportions. If the lengths of the triangles are given as 1 inch to 50 inches and 0.5 inches to 5 inches, we can set up the proportion 1/50 = 0.5/5 to show that they are equivalent.
In problems like this, proper notation and maintaining consistency across corresponding dimensions (e.g., width to width and length to length) is essential for accurate comparison.
Given f (x). find g(x) and h(x) such that f(x) = g(h(x)) and neither g(x) nor h(x) is solely x.
f(x)=
[tex] \sqrt{ - 2 {x}^{2} + 3 } - 5[/tex]
find g(x) and h(x)
[tex]g(x)=\sqrt x-5\\h(x)=-2x^2+3[/tex]
find the area of the parallelogram answer option 15 25 30 44
There is no picture of the parallelogram needed to answer this question.
Examine the quadratic equation: x^2+2x+1=0
A: What is the discriminant of the quadratic equation?
B: Based on the discriminant, which statement about the roots of the quadratic equation is correct?
Select one answer choice for question A, and select one answer choice for question B.
A: 3
A: 0
A: −3
B: There is one real root with a multiplicity of 2 .
B: There are two real roots.
B: There are two complex roots
Answer:
A: 0
B: There is one real root with a multiplicity of 2.
Step-by-step explanation:
[tex]\bf{x^2+2x+1=0}[/tex]
A:The discriminant of the quadratic equation can be found by using the formula: [tex]b^2-4ac[/tex].
In this quadratic equation,
a = 1b = 2c = 1I found these values by looking at the coefficient of [tex]x^2[/tex] and [tex]x[/tex]. Then I took the constant for the value of c.
Substitute the corresponding values into the formula for finding the discriminant.
[tex]b^2-4ac[/tex][tex](2)^2-4(1)(1)[/tex]Simplify this expression.
[tex](2)^2-4(1)(1)= \bf{0}[/tex]The answer for part A is [tex]\boxed{0}[/tex]
B:The discriminant tells us how many real solutions a quadratic equation has. If the discriminant is
Negative, there are no real solutions (two complex roots).Zero, there is one real solution.Positive, there are two real solutions.Since the discriminant is 0, there is one real root so that means that the first option is correct.
The answer for part B is [tex]\boxed {\text{There is one real root with a multiplicity of 2.}}[/tex]
Answer:
A: 0
B: There is one real root with a multiplicity of 2 .
Step-by-step explanation:
Given a quadratic equation:
[tex]ax^2+bx+c=0[/tex]
You can find the Discriminant with this formula:
[tex]D=b^2-4ac[/tex]
In this case you have the following quadratic equation:
[tex]x^2+2x+1=0 [/tex]
Where:
[tex]a=1\\b=2\\c=1[/tex]
Therefore, when you substitute these values into the formula, you get that the discriminant is this:
[tex]D=(2)^2-4(1)(1)\\\\D=0[/tex]
Since [tex]D=0[/tex], the quadratic equation has one real root with a multiplicity of 2 .
NEED HELP with this word problem ASAP!
Answer:
[tex]t=280\ minutes[/tex]
Step-by-step explanation:
Let's call "v" the speed of the commercial airplane and call "t" at the travel time of the commercial plane
The distance in kilometers of the trip is: 1730 km
Then we know that:
[tex]vt=1730[/tex]
Then for the jet we have that the speed is:
[tex]2v[/tex]
The flight time for the jet is:
[tex]t-140[/tex]
Therefore:
[tex](2v)(t-140) = 1730[/tex]
Substituting the first equation in the second we have to:
[tex](2*\frac{1730}{t})(t-140) = 1730[/tex]
[tex](\frac{3460}{t})(t-140) = 1730[/tex]
[tex]3460-\frac{484400}{t} = 1730[/tex]
Now solve for t
[tex]\frac{484400}{t} = 3460 - 1730[/tex]
[tex]\frac{484400}{t} =1730[/tex]
[tex]\frac{t}{484400} =\frac{1}{1730}[/tex]
[tex]t=\frac{484400}{1730}[/tex]
[tex]t=280\ minutes[/tex]
the values in the table represent a linear function. what is the common difference of the associated arithmetic sequence?
x: 1, 2, ,3 ,4 ,5
y: 6, 22, 38, 54, 70.
A) 1
B) 20
C) 16
D) 5
Answer:
c
Step-by-step explanation:
You can find that 22-6=38-22=54-38=70-54=16
so the answer is c 16
Answer: The correct opion is
(C) 16.
Step-by-step explanation: Given that the values in the following table represent a linear function.
x: 1, 2, 3, 4, 5
y: 6, 22, 38, 54, 70.
We are to find the common difference of the associated arithmetic sequence.
If y = f(x) is the given function, then we see that
f(1) = 6, f(2) = 22, f(3) = 38, f(4) = 54 and f(5) = 70.
So, the common difference of the associated arithmetic sequence is given by
[tex]f(2)-f(1)=22-6=16,\\\\f(3)-f(2)=38-22=16,\\\\f(4)-f(3)=54-38=16,\\\\f(5)-f(4)=70-54=16,~~~\cdots.[/tex]
Thus, the required common difference of the associated arithmetic sequence is 16.
Option (C) is CORRECT.
5/6 n=10 what is n in this equation
If i^2 = −1 and a = (i + 7), which is the result of squaring a?
Answer:
48+14i
Step-by-step explanation:
So squaring (i+7) looks like this
(i+7)^2
(i+7)(i+7)
Use foil.
First: i(i)=i^2=-1
Outer: i(7)=7i
Inner: 7(i)=7i
Last: 7(7)=49
____________Add the terms.
48+14i
After solving the expression, the result of squaring value of a will be equal to 14i + 48.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the data provided by the question,
i² = -1
a = (i + 7)
Squaring the value of a,
a = (i + 7)(i + 7)
a = i² + 7i + 7i +49
a = -1 + 14i + 49
a = 14i +48
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19.) Here's the data (sorted) of the ages of 91 women who won the Oscar for Best Actress in a Leading Role:
21, 22, 22, 24, 24, 24, 24, 25, 26, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 31, 31, 31, 32, 32, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 37, 37, 37, 37, 38, 38, 38, 39, 39, 39, 41, 41, 41, 41, 42, 42, 44, 45, 45, 45, 47, 49, 49, 54, 60, 60, 61, 61, 61, 62, 62, 74, 81
Give the five number summary.
Final answer:
The five number summary for the ages of best actress Oscar winners is composed of the minimum (21), first quartile (Q1 - 30), median (Q2 - 33), third quartile (Q3 - 41), and maximum (81) values.
Explanation:
The first step to finding the five number summary is to identify the minimum, first quartile (Q1), median (second quartile Q2), third quartile (Q3), and the maximum from the sorted dataset of best actress Oscar winners.
Minimum: The smallest number in the dataset is 21.
Q1: The first quartile is the median of the first half of the data. Since we have an odd number of data points (91), we split the data into two parts of 45 values each. The first quartile is the median of the first 45 ages, which is the 23rd data point in the sorted list when counting from the smallest age. In our case, Q1 is 30.
Median (Q2): The median is the middle value, which is the 46th data point for our 91 data points. The median is also the age of 33.
Q3: The third quartile is the median of the second half of the data. The third quartile is the 68th data point, which is the age of 41.
Maximum: The largest age in the dataset is 81.
Therefore, the five number summary of the ages of best actress Oscar winners is 21, 30, 33, 41, and 81.
Rectangle ABCD is shown on the grid.
The area of rectangle ABCD in square units is_____ .
Anyone know how to do this math problem and if so could you please take your time to explain it in the comments below thank you!
Answer:
34 square units
Step-by-step explanation:
Step 1 : Write the formula for area of rectangle
Area of rectangle = length x breadth
From the graph:
AB = DC
AD = BC
Step 2 : Find the distance between AB and AD to find the length and breadth.
Coordinates : A (-1, 4), B (3, 3)
Distance between two points on AB
Formula : √(x2-x1)² + (y2-y1)²
= √(3-(-1))² + (3-4)²
= √17
Distance between two points on AD
Coordinates of A (-1, 4), D = (-3,-4)
Formula : √(x2-x1)² + (y2-y1)²
= √(-3-(-1))² + (-4-4)²
= √68
Area of rectangle = length x breadth
Area of rectangle = √17 x √68
Area of rectangle = 34
Therefore the area of rectangle = 34 square units
!!
Answer:
34
Step-by-step explanation:
define the radius of a circle
Answer: The radius is the distance between the center and the circumference of a circle and is half of the diameter of the circle .
Hopefully, this helps!
A line segment that joins the center of a circle to any point on the circle is called the radius of the circle. Whichever point on the circle we choose, the distance to the center of the circle will always be the same.
What is the coefficient of x3y2 in the expansion of (2x + y)5?
Step-by-step answer:
The coefficients of terms of (p+q)^n can be found by the Pascal's triangle for small values of n. Pascal's triangle will start with (1,1) = coefficients of (p,q)^n =1. For n=2, we add successive terms of the previous value of n. Thus for n-2, we have (, 1+1,11=(1,2,1), for n=3, we have (1,3,3,1), giving the following pattern:
(1,1)
(1,2,1)
(1,3,3,1)
(1,4,6,4,1)
(1,5,10,10,5,1)
meaning for n=5, the binomial expansion for (P+Q)^5 is
P^5+5P^4Q+10P^3Q^2+10P^2Q^3+5PQ^4+Q^5
Setting P=2x, Q=y in the term 10P^3Q^2, we get a term
10(2x)^3(y)^2
=10(8x^3)(y^2)
=80x^3y^2
So the required coefficient is K=80.
We can also find the coefficient 10 by binomial expansion of
n=5, x=3 in
C(n,x) = n! / (x! (n-x)!) = 5! / (2!3!) = 5*4*3/(1*2*3) = 10
Then again substituting 10(2x)^3(y)^2 = 80x^3y^2
to get the coefficient K=80.
Answer: 80
Step-by-step explanation: cuz
Kayla rolls a die 84 times. How many times can she expect to roll a 3?
Answer:
14
Step-by-step explanation:
Assuming the die is 6 sided, there are only 6 possible rolls she can get. And assuming that this is a perfect world where probability is perfect, she will roll each number 14 times, because 84/6 is 14.
Final answer:
Kayla can expect to roll a number 3 approximately 14 times out of 84 rolls of a fair six-sided die, since each roll has a 1 in 6 chance of landing on any given number.
Explanation:
When Kayla rolls a die 84 times, she can expect to roll a 3 in a proportion equal to the probability of rolling a 3 on a single die. A fair six-sided die has a 1 in 6 chance of landing on any given number, including the number 3. Since each roll of the die is independent, we can calculate the expected frequency of rolling a 3 by multiplying the total number of rolls by the probability of rolling a 3.
The calculation is straightforward:
Probability of rolling a 3 = 1/6.Expected frequency of rolling a 3 = Total number of rolls × Probability of rolling a 3.Expected frequency of rolling a 3 = 84 × (1/6) = 14.Therefore, Kayla can expect to roll a 3 approximately 14 times in 84 rolls.
The net of a square pyramid is shown:
Answer:
The surface area of the pyramid is 0.6625 inches²
Step-by-step explanation:
* Lets explain how to find the surface area of the square pyramid
- The square pyramid has 5 faces
- A square base
- Four triangular faces
- Its surface area is the sum of the areas of the five faces
- Area of the square = L × L , where L is the length of its sides
- Area of the triangle = 1/2 × b × h , where b is the length of its base
and h is the length of its height
∵ The length of the side of the square is 0.25 inches
∴ Area of the base = 0.25 × 0.25 = 0.0625 inches²
∵ The length of the base of the triangle is 0.25 inches and the length
of its height is 1.2 inches
∴ The area of its triangular face = 1/2 × 0.25 × 1.2 = 0.15 inches²
∵ The surface area of the pyramid = the sum of the areas of the 5 faces
∵ The area of the four triangular faces are equal
∴ The surface area = 0.0625 + (4 × 0.15) = 0.0625 + 0.6
∴ The surface area = 0.6625 inches²
* The surface area of the pyramid is 0.6625 inches²
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What is the average rate of change for this function for the interval from x = 2
to x = 4?
Answer:
D
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ 2, 4 ]
From the table
f(b) = f(4) = 16
f(a) = f(2) = 4, hence
average rate of change = [tex]\frac{16-4}{4-2}[/tex] = [tex]\frac{12}{2}[/tex] = 6
The average rate of change for a function is calculated using the change in y-values divided by the change in x-values.
Explanation:The average rate of change for a function is the change in the y-values (output) divided by the change in the x-values (input) over a given interval. To calculate the average rate of change for the function from x = 2 to x = 4, we need to find the change in y-values and the change in x-values for this interval.
Let's assume the function is f(x). We can calculate the average rate of change using the formula:
Average Rate of Change = (f(4) - f(2)) / (4 - 2)
Replace f(4) and f(2) with the corresponding y-values for x = 4 and x = 2, respectively, to get the final result.
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HELP me please !! I really need it
Answer:
D
Step-by-step explanation:
To find the critical values , that is the zeros
Solve the quadratic
x² - x - 20 = 0 ← in standard form
Consider the factors of the constant term (- 20) which sum to give the coefficient of the x- term (- 1)
The factors are - 5 and + 4, since
- 5 × 4 = - 20 and - 5 + 4 = - 1, hence
(x - 5)(x + 4) = 0
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 4 = 0 ⇒ x = - 4
Thus the critical values are - 4, 5 → D
Answer:
D. -4, 5
Step-by-step explanation:
x² - x - 20 factorised = (x - 5) (x + 4)
In order to get the answers, you have to make each bracket equal zero.
(x - 5) = x = 5
(x + 4) = x = -4
The crucial numbers are -4 and 5.
Hope this helps!
1. Solve the equation m2 + 6m=-4 using the quadratic formula.
A. m = 5+3
O B. m = 3+V 5
c. m =-3+1 5
D.m=-5+13
Answer:
-3± √5
Step-by-step explanation:
It is given that,
m² + 6m = -4
Points to remember
Solution of a quadratic equation ax² + bx + c = 0
x = [-b ± v(b² - 4ac)]/2a
To find the solution of given equation
m² + 6m = -4
⇒ m² + 6m + 4 = 0
Here a = 1, b = 6 and c = 4
m = [-b ± v(b² - 4ac)]/2a
= [-6 ± √(6² - 4*1*4)]/2*1
= [-6 ± √(36 - 16)]/2
= [-6 ± √20]/2
= [-6 ± 2√5]/2
= -3± √5
What is the area of the trapezoid
O 120in
O 140in
O 91in
O 182in
Answer:
A = 91 in²Step-by-step explanation:
The formula of an area of a trapezoid:
[tex]A=\dfrac{b_1+b_2}{2}\cdor h[/tex]
b₁, b₂ - bases
h - height
We have b₁ = 20in, b₂ = 6in and h = 7in.
Substitute:
[tex]A=\dfrac{20+6}{2}\cdot7=\dfrac{26}{2}\cdot7=(13)(7)=91\ in^2[/tex]
What is the least common multiple of 4 and 6?
Answer:
12
Step-by-step explanation:
Consider the list of multiples
multiples of 4 are 4, 8, 12, 16, 20, ....
multiples of 6 are 6, 12, 18, 24, ....
The least common multiple is 12
can someone help me solve this step by step? tyyyy
Answer:
x=4/7
Step-by-step explanation:
6 - 2/3(x+5) = 4x
First I want to clear the fraction so I will multiply everything by 3
3*6 -3* 2/3(x+5) = 3*4x
18 - 2(x+5) =12x
Distribute
18 - 2x-10 =12x
Combine like terms
8 -2x = 12x
Add 2x to each side
8 -2x+2x =12x+2x
8 = 14x
Divide each side by 14
8/14 =14x/14
8/14=x
Divide top and bottom by 2
4/7=x
help with 1-10 , please!!!!!!
Step-by-step explanation:
hi I have answered ur question
Answers:
1. 75/w=5/6
5*w=75*6
5w=450
Divide by 5 for 5w and 450
5w/5=450/5
w=90
2. 1/5=11/p
1*p=5*11
p=55
3. 9/z=3/13
3z=13*9
3z=117
Divide by 3 for 3z and 117
3z/3=117/3
z=39
4. 210=15m
Divide by 15 for 210 and 15m
210/15=15/15m
m=14
5. 22n=11*19
22n=209
22/22n=209/22
n=9.5
6. 9p=180
9p/9=180/9
p=20
7. 100=5x
100/5=5x/5
x=20
8. 4*x=3*24
4x=72
x=18
9. 10*y=14*7
10y=68
10y/10=68/10
y= 68/10
10. 16x=8*15
16x=120
16x/16=120/16
x=7.5
Y intercept 3 and a slope of -6
Answer:
y=-6x+3
Step-by-step explanation:
Answer:
y=-6x+3
Step-by-step explanation:
because the slope will always have the X and in the middle you can put them together to get your answer
can u help me wit A, B, C, and D
And can you explain which statement would have the largest answer on the four choices
Answer:
D is 36080
Step-by-step explanation:
D is the largest since A is 3.608, B is 360.8, C is 36.08
When dividing, the smaller decimal points will be larger, but if you multiple, the numbers shrink.
Consider the vectors u <-4,7> and v= <11,-6>
See picture for more information. Please help
Answer:
u + v = <7 , 1>
║u + v║ ≅ 7
Step-by-step explanation:
* Lets explain how to solve the problem
- We can add two vector by adding their parts
∵ The vector u is <-4 , 7>
∵ The vector v is <11, -6>
∴ The sum of u and v = <-4 , 7> + <11 , -6>
∴ u + v = <-4 + 11 , 7 + -6> = <7 , 1>
∴ The sum u and v is <7 , 1>
* u + v = <7 , 1>
- The magnitude of the resultant vector = √(x² + y²)
∵ x = 7 and y = 1
∵ ║u + v║ means the magnitude of the sum
∴ The magnitude of the resultant vector = √(7² + 1²)
∴ The magnitude of the resultant vector = √(49 + 1) = √50
∴ The magnitude of the resultant vector = √50 = 7.071
* ║u + v║ ≅ 7
Need to find A, B, and C!
Answer:
Mean: 4.44 add up every number and divide it by how many there is.
Median: 3 put from least to greatest and count till the middle.
Mode: 3 because it appears the most
Answer:
A. Mean = $41900
B. Median = $37000
C. Mode = $37000
Step-by-step explanation:
A. Mean
Here
n=40
Mean = Sum of values/n
[tex]Mean = \frac{(3)(18000)+(3)(22000)+(3)(25000)+(5)(34000)+(17)(37000)+(2)(45000)+52000+(5)(80000)+140000}{40}\\=\frac{54000+66000+75000+170000+629000+90000+52000+400000+140000}{40} \\=\frac{1676000}{40}\\=41900[/tex]
Mean = $41900
B. Median:
As the number of salaries is even,
the median will be mean of middle two terms
[tex]Median= \frac{1}{2}(\frac{n}{2}th\ term+ \frac{n+2}{2}th\ term)\\= \frac{1}{2}(\frac{40}{2}th\ term+ \frac{40+2}{2}th\ term)\\=\frac{1}{2} (20th + 21st)}\\[/tex]
The 20th and 21st term will be 37000
So their mean will be same
So,
Median = $37000
C. Mode
Mode is the value which occurs most of the time in data.
the occurrence of 37000 is highest in the given data.
So,
Mode = $37000 ..
Find angle measures and use angles to classify triangles.
Answer:
1) 55 degrees
2) 90 degrees
3) 105 degrees
Step-by-step explanation:
All triangles equal to 180 degrees. So to find the missing angle measure you have to subtract the two given measures by 180.
First triangle:
180 - 50 - 75 = 55 degrees
Second triangle:
180 - 60 - 30 = 90 degrees
Third triangle:
180 - 45 - 30 = 105 degrees
Which rotation maps point K(8,-6) to K(-6, -8)?
Answer:
90 degree clockwise rotation about (0,0).
Step-by-step explanation:
That would be a clockwise rotation of 90 degrees about the origin (0,0).
The rotation that maps point K(8,-6) to K(-6,-8) is a counterclockwise rotation of 90 degrees about the point (0,0).
What is the transformation of geometry over the coordinate plane?Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.
Here,
To find the rotation that maps point K(8,-6) to K(-6,-8), we can use the following steps,
Plot the points K(8,-6) and K(-6,-8) on a coordinate plane.
Since point K(8,-6) is being mapped to point K(-6,-8), the rotation must be counterclockwise. As rotation about the origin with angle 90 gives the transformation equation,
(x, y) ⇒ (y, -x)
Therefore, the rotation that maps point K(8,-6) to K(-6,-8) is a counterclockwise rotation of 90 degrees about the point (0,0).
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